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Regeneration‐based bootstrap for Markov chains
Author(s) -
Datta Somnath,
Mccormick William P.
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315810
Subject(s) - markov chain , mathematics , combinatorics , statistics
We consider a bootstrap method for Markov chains where the original chain is broken into a (random) number of cycles based on an atom (regeneration point) and the bootstrap scheme resamples from these cycles. We investigate the asymptotic accuracy of this method for the case of a sum (or a sample mean) related to the Markov chain. Under some standard moment conditions, the method is shown to be at least as good as the normal approximation, and better (second‐order accurate) in the case of nonlattice summands. We give three examples to illustrate the applicability of our results.